The second result about uniqueness of SDE in a poor regularity setting is due to Athreya, Bhar and Shekhar [1]} when \(\mathbf {w}\)  is the fractional Brownian motion rough path (for \(H>\frac{1}{3}\) ). There strategy is to make Lamperti transform to get back to an additive problem, and then to use the result of [2]}. To do so, whereas in dimension \(d=1\)  this strategy works pretty well, in dimension \(d\ge 2\)  one has to ask that \(\sigma ^{-1}\)  is conservative. This is a huge restriction, since one could expect that \(\sigma \)  stricly-elliptic would be sufficient.
